N.H. Rev. Stat. Ann. § 594:18-a

When a peace officer makes an arrest without a warrant, either he or his superior officer may release the person arrested instead of taking him before a district or municipal court if satisfied either that there is no ground for making a criminal complaint against such person or that such person has been arrested for drunkenness and no further proceedings are necessary. A person released as above provided shall have no right to sue any peace officer on the ground that he was released without being brought before a court.